Online Reviews and Collaborative Service Provision: A...

Online Reviews and Collaborative Service Provision:A Signal-Jamming Model

Haoying SunDepartment of Marketing & Supply Chain, Gatton College of Business and Economics, University of Kentucky, 550 South Limestone,

Lexington, Kentucky 40506, USA, [email protected]

Lizhen XuScheller College of Business, Georgia Institute of Technology, Atlanta, Georgia 30308, USA, [email protected]

W e study the provision of collaborative services under online reviews, where the service outcome depends on theeffort of both the service provider and the client. The provider decides not only her own effort but also the client’s,

at least to some extent. The client gives the review based on his net utility upon service completion. We develop a signal-jamming model in which the provider’s inherent capability or type is unobservable, and the market infers the providertype through observable signals such as the service outcome, the client review, or both. We show that compared to thebenchmark case when the service outcome is observed as a signal, the client review generally leads to less effort of boththe provider and the client. The review hence tends to sacrifice the service effectiveness in favor of the efficiency of theclient’s effort input. Nevertheless, when clients incorporate private information about the provider type into their reviews,service providers are better motivated to devote effort. Interestingly, we find the provider’s effort choices may be eitherstrategic complements or substitutes. With a reasonable level of informativeness, online reviews could lead to favorableperformance in service effectiveness, client effort efficiency, and provider type distinguishability. Surprisingly, we demon-strate that when both the review and the outcome are available, the provider may lack sufficient incentive to devote effort,resulting in inferior distinguishability of provider types. It thus illustrates that richer information may not necessarily gen-erate favorable strategic outcomes.

Key words: online review; collaborative service; signal jamming; educational service; bivariate signalHistory: Received: April 2015; Accepted: May 2016 by Vijay Mookerjee, after 2 revisions.

1. Introduction

Online reviews of services, in which customers rateand recommend various service providers (e.g., per-sonal tutors, professional consultants), have becomepervasive in recent years, as various ecommerce web-sites, user-generated-content platforms, and socialnetworks all facilitate customers to review their ser-vice experiences (e.g., nextdoor.com, kudzu.com,elance.com). Thanks to the advancement of informa-tion systems and the ubiquitous access to the Internet,online repositories of customer reviews enable theseotherwise hard-to-observe information to disseminateacross spatial and temporal boundaries to becomeavailable to the general public, generating profoundinfluences on business. Nevertheless, although a largevolume of literature has been devoted to studyingonline reviews of products, surprisingly, onlinereviews of services have been left mostly untouched

in the existing literature. We hence aim to fill this gapby taking an early step to theoretically explore howonline reviews could impact service provision.Within the huge service industry, one type of ser-

vices that particularly draws our research interest isthe educational and tutoring services (e.g., coachingstudents for standardized tests, teaching ice skating).As a rapidly growing industry, it is estimated that theglobal private tutoring market will reach $200 billionby 2020 (GIA 2014). Given the sophistication of educa-tional activities and their lasting impacts, it is espe-cially critical to distinguish superior providers of thistype of services. A recent study shows empirical evi-dence that a good teacher can increase the presentvalue of students’ lifetime income by hundreds ofthousands of dollars (Chetty et al. 2014). Naturally,we see a proliferation of online review platforms (e.g.,nextdoor.com, myedu.com) that serve to help usersidentify and recommend high-quality providers ofsuch services.Apart from the industrial importance, the nature of

the educational and tutoring services makes it espe-cially intriguing to study the associated strategic

[Correction added on 31 May 2018, after first onlinepublication: the affiliation and email address of HaoyingSun have been changed.]

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Vol. 27, No. 11, November 2018, pp. 1960–1977 DOI 10.1111/poms.12592ISSN 1059-1478|EISSN 1937-5956|18|2711|1960 © 2016 Production and Operations Management Society

interplay under online reviews. First, this type of ser-vices is collaborative, because the outcome of the ser-vice depends on not only the effort of the serviceprovider but the effort of the client as well. Moreover,the service provider not only decides her own effortinput but also determines the effort level of the client,at least to a certain extent (e.g., a tutor typically speci-fies the amount of exercise a student is required totake). As both effort levels are not directly observableto outsiders, two-dimensional moral hazard exists,and the service provider’s strategic choice of thesetwo hidden actions is thus a key issue to explore.Considering that the effort level set for the clientdirectly affects the client’s utility, will the service pro-vider intentionally allow the client to shirk inexchange for a higher level of “happiness” and thus abetter review? Consequently, will online reviews leadto strategic deterioration of the service performance?Furthermore, given the collaborative nature, thestrategic correlation between the two effort decisionsis another question of interest. With the client reviewin consideration, will the service provider investexcessive effort herself in place of the effort requiredfrom the client, or will the service provider choose toshirk as a result of the limitation on pushing the clientto work diligently enough? In this sense, will the twoeffort choices strategically substitute or complementeach other under online reviews? This study isintended to shed light on these questions.Besides the unobservable actions, the inherent

capability of a service provider to effectively deliverthe service is also unobservable, making distinguish-ing the superior provider another important questionworth examining. Different from the usual case of sig-naling game in which a provider can signal her supe-riority through observable actions, in this context,prospective clients (more generally, the market) caninfer the capability of a service provider only throughcertain observable signals, which, in turn, can bemanipulated by the hidden actions strategically cho-sen by the service provider. Meanwhile, the marketshould rationally anticipate such strategic plays andproperly adjusts the belief in equilibrium. It thus con-stitutes the classical signal-jamming problem (Fuden-berg and Tirole 1986). Being informative about theinherent capability of the provider, online reviewscan certainly serve as such a signal, whose effects onservice provision hence deserve careful analysis.Another natural candidate for such a signal is the out-come of the service itself.1 Depending on their avail-ability, either the service outcome or the client review,or both, can be observed by the market. We thus usethe service outcome as a benchmark case to contrastwith the cases when the market observes the clientreview either alone or along with the service outcome.We are interested in comparing the resulting

performance of the strategic service provision and thedistinguishability of the service provider’s underlyingcapability.While motivated from the context of educational

and tutoring services, our model and results havegeneral implications for other types of services withsimilar features, as long as the service is collaborativein nature, the service provider can determine (at leastto a certain extent) the effort level of the client, andthe service outcome is objective. Examples includeconsulting services (e.g., IT consulting projects requir-ing collaboration from both parties), professional ser-vices (e.g., taxation and auditing, legal services), andhealth care services (e.g., rehabilitation and physicaltherapy).In this study, we develop a signal-jamming model

and compare the equilibrium effort levels when theservice outcome is observed as a signal and whenthe client review serves as a signal. We find that thereview generally leads to a lower effort level for theclient, as the provider is concerned about the client’sdisutility of exerting effort to be negatively reflectedin the review. Meanwhile, the review does lead to anefficient effort level for the client, that is, the sameeffort level the client would have chosen for himself.For the provider’s own effort decision, we identifytwo effects determining the provider’s incentive foreffort investment, namely, the affirmative effect andthe informative effect. The former refers to how likelythe effort input can result in a positive signal,whereas the latter means how convincingly a positivesignal implies the superiority of the provider. Weshow that under online reviews, two factors—theadditional uncertainty of the review and the lowereffort from the client—weaken both affirmative andinformative effects, resulting in a lower effort level ofthe provider. In this sense, the client review results ina sacrifice of the service outcome in favor of the cli-ent’s utility, which leads to a lower degree of distin-guishability of the provider type in equilibrium.We further extend the analysis by allowing the cli-

ent to observe private information about the providertype upon service completion and to incorporate suchinformation into his review. As a result, the informa-tive effect is strengthened, and the provider is bettermotivated to work diligently. Interestingly, when thereview is highly informative, the provider’s two-dimensional effort decisions may be strategic substi-tutes in that the provider requires less effort from theclient compared to the benchmark case, yet sheinvests excessive effort of her own. As we show, witha reasonable level of informativeness, online reviewscould lead to favorable equilibrium performance inmultiple dimensions: higher service effectiveness,more efficient effort level for the client, and better dis-tinguishability of the provider type.

Sun and Xu: Online Reviews and Collaborative ServicesProduction and Operations Management 27(11), pp. 1960–1977, © 2016 Production and Operations Management Society 1961

We also investigate the case in which the clientreview is observable along with the service outcome.Counterintuitively, we demonstrate that richer infor-mation may not necessarily generate favorable resultsas an outcome of strategic interplay. When both thereview and the outcome are observable to the market,the service provider surprisingly lacks sufficientincentive to devote effort, simply because the bivari-ate signal structure makes a successful service out-come no longer rewarding if the review is negative.As a result, both signals being available at the sametime could lead to inferior distinguishability of provi-der types.To the best of our knowledge, this study is the first

theoretical study connecting online reviews with col-laborative services. From modeling perspective, adistinctive aspect of our study is that we introducethe signal-jamming framework into the context ofonline reviews and service management, whichenables us to explicitly model the review generatingand information updating processes and to endoge-nously incentivize effort input without externalagency contracts. Our results also enrich the infor-mation economics by illustrating how strategic inter-play under a complex information structure can leadto surprising economic consequences. On the sub-stantive front, the findings in this study provide richimplications for various stakeholders, includinginformation systems designers, top management andauthorities, service providers, and clients who writereviews, as we discuss in detail in the end of thearticle.

2. Literature Review

As we study the unique information structure associ-ated with online reviews in the context of collabora-tive services, our modeling approach is rooted in theclassical signal-jamming framework (Fudenberg andTirole 1986, Holmstrom 1999). The problem we studyand the modeling approach we adopt are thus distinctfrom what is typically found in the existing literatureon both online reviews and collaborative services, aswe briefly review below.The existing literature on online reviews predomi-

nantly focuses on customer reviews of products.There is a large volume of literature empirically inves-tigating how different aspects of online reviews affectthe sales of various products such as books (e.g., Che-valier and Mayzlin 2006), movies (e.g., Liu 2006),video games (e.g., Zhu and Zhang 2010), and digitalcameras (e.g., Gu et al. 2012). Meanwhile, theoreticalstudies develop analytical models to examine howproduct reviews could affect product sales (e.g., Liand Hitt 2010), firm strategies (e.g., Chen and Xie2008), and market competition (e.g., Kwark et al.

2014). Recent literature (e.g., Jiang and Guo 2015) fur-ther explores the optimal design of review systemswith endogenous consideration of product featuressuch as product mainstream level and consumer mis-fit cost. Studying reviews of services, we thus differfrom the extant literature in the research context andthe main focus.In modeling the role of online reviews, the afore-

mentioned theoretical papers typically view it as con-veying product information and generally take one ofthe two approaches. One class of approach (e.g., Chenand Xie 2005, 2008, Kwark et al. 2014) considersreviews as an exogenous information source provid-ing additionally accurate information about productquality and/or fit, where the review generating pro-cess is left exogenous. Another class of approach (e.g.,Hao et al. 2011, Jiang and Guo 2015, Sun 2012) modelsthe generation of reviews as a deterministic functionof customer utility involving observable information(e.g., price) and individual reviewer heterogeneity.As a result, rational prospective customers can backout the product information (e.g., quality, fit) basedon the observable information (e.g., valence and vari-ance of reviews, price). Differently, we not onlyendogenously model the review generating and infor-mation updating processes, but also account for theeffects of hidden strategic actions and possible noises.In consequence, how accurately the review can con-vey information about the latent provider ability is astrategic outcome endogenously dependent on theinformation structure, and reviews may not necessar-ily lead to more accurate information in equilibrium.In this sense, our modeling approach is close to Kuk-sov and Xie (2010). They consider a two-period modelof product reviews conveying information about thelatent product quality, which both the firm and cus-tomers are unsure of. The firm strategically decidesthe price and the “frill”, both unobservable to the sec-ond-period customers, to influence the reviews givenby the first-period customers. Besides the differentresearch context, the information structure studied inour study is also different from theirs in that we intro-duce an additional layer of uncertainty into thereview, so it depends on another random variable(i.e., the service outcome). Consequently, we can fur-ther study the effects when both signals are observ-able and discover interesting equilibrium results.More broadly, our study is also related to another

stream of literature on reputation (e.g., Bakos andDellarocas 2011, Kreps and Wilson 1982, Milgromand Roberts 1982), which takes the view that reputa-tion is built and maintained as an indication of credi-ble commitment (i.e., being locked into playing acertain strategy) in repeated games. In contrast, simi-lar to the aforementioned theoretical papers on pro-duct reviews, our study emphasizes the role of

Sun and Xu: Online Reviews and Collaborative Services1962 Production and Operations Management 27(11), pp. 1960–1977, © 2016 Production and Operations Management Society

reviews as revealing additional information aboutunderlying key characteristics (i.e., ability). In addi-tion to the different fundamental views, other distinc-tions include: we endogenously model the generationof reviews, which depend on service outcomes andstrategic actions as well, whereas reputation is typi-cally considered as a direct collection or an externally-specified transformation of past performances; wecompare equilibrium results under different signals,which, in a broad sense, provides richer implicationsfor the effects of different reputation mechanisms;moreover, we link online reviews to collaborative ser-vices, filling a gap between these two important areas.Starting from Karmarkar and Pitbladdo (1995), col-

laborative (or coproductive) services have been attract-ing increasing research interest in the literature ofoperations management (e.g., Plambeck and Taylor2006, Roels et al. 2010, Spohrer and Maglio 2008, Xueand Field 2008) as well as information technology out-sourcing (e.g., Bhattacharya et al. 2014, Demirezenet al. 2013). The extant literature in this domain pre-dominantly follows the principal-agent contract-design framework. In contrast, as we study a newproblem in this context, we build upon the theories ofcareer concerns (Holmstrom 1999) and allow the ser-vice provider to be incentivized endogenously withoutexternally stipulated agency contracts or in the face ofpossible incomplete contracts. Another difference isthat the service provider also determines the client’seffort in addition to her own in our context, whichincreases the dimension of the provider’s strategyspace and leads to interesting strategic correlation.

3. The Baseline Model

3.1. Model SetupWe consider one service provider and one client inthe market.2 The service is collaborative, and the out-come of the service depends on the effort levels ofboth the service provider and the client. We denotethe effort level of the service provider as x and that ofthe client as y, where both are bounded and normal-ized such that x, y 2 [0, 1]. In addition, the serviceoutcome is also influenced by the innate ability of theservice provider to deliver the service effectively,which we refer to as the type of the provider. Weassume there are two types of the service provider,high (H) type or low (L) type, where a high-type pro-vider is more likely to deliver the service effectivelythan a low-type provider given the same effort levels.Besides these focal factors, many other factors notdirectly pertinent to our interest may also affect theoutcome. Therefore, the outcome is probabilistic byits nature. We hence model the outcome of the ser-vice, V, as a random variable taking a binary value, 0or 1, where 1 represents success (e.g., passing a

standardized test, achieving the preset goal) and 0represents failure. The value of V depends on a latentvariable m, which represents the combination of allpossible factors affecting the service outcome. If m > 0,we have V = 1; if m ≤ 0, we have V = 0. Specifically, mis modeled as follows.

m n; h; x; yð Þ ¼ lh xþ yð Þ þ n; h 2 H; Lf g: ð1ÞHere, lh reflects the innate ability of the h-type pro-vider, and 0\ lL \ lH. Without loss of generality,we normalize lH ¼ 1 and let lL ¼ l 2 ð0; 1Þ. Theterm (x + y) represents the combined effort fromboth parties, which captures the collaborative natureof the service and is commonly used in the literature(e.g., Karmarkar and Pitbladdo 1995). The last termin (1), ξ, represents other idiosyncratic factors thatcould possibly affect the service outcome. It is a ran-dom variable with the cumulative distribution func-tion (cdf) G(ξ). To derive clean analytical results, welet ξ follow a uniform distribution over the support[�2, 0], so GðnÞ ¼ nþ 2

2 . The support is chosen suchthat when the deterministic term lhðx þ yÞ takes itsminimum value 0, we have m(ξ) ≤ 0 for any possibleξ; when lhðx þ yÞ takes its maximum value 2, wehave m(ξ) ≥ 0 for all ξ ’s. Notice that neither the dis-tribution nor the support of ξ is critical for ourresults to hold. As we show in Appendix S2, underdifferent distributions (e.g., beta distribution, normaldistribution) or expanded supports (either finite orinfinite), our main results remain robust.

As a result, the probability of the outcome being asuccess, given the true type of the service providerand the effort levels of both parties, can be derived as

Pr V ¼ 1jh; x; yf g ¼ Pr m nð Þ[ 0jh; x; yf g¼ 1� G �lh xþ yð Þð Þ¼ 1

2lh xþ yð Þ; h 2 H; Lf g:

ð2Þ

After exerting the effort y and observing the rea-lized outcome V, the client derives net utilityUðV; yÞ ¼ u1V¼1 � wy2, where 1V¼1 is an indicatorfunction such that 1V¼1 ¼ 1 if V = 1, and 1V¼1 ¼ 0otherwise. In other words, the client derives positiveutility gain u if the outcome turns out a success andzero utility gain if a failure; meanwhile, the utility costfrom exerting effort is wy2. Here, w is the client’s effortcost coefficient (0 < w < u), and the convex functionalform captures the increasing marginal disutility as theeffort level increases. Without loss of generality, wenormalize u = 1, and thus w 2 (0, 1).Given the realized utility, the client then writes an

online review of the service provider. Consideringthat various latent factors could all affect the review(e.g., leniency, preference), we adopt a similar


structure as the outcome and model the review, R, asa random variable taking a binary value: R = 1 meansthe client recommends the service provider, and R = 0means he does not recommend. The binary structurereflects the commonly observed rating mechanismused in online reviews and is also common in theliterature (e.g., Kuksov and Xie 2010). For easy refer-ence, we refer to R = 1 as a positive review and R = 0 anegative review. The value of R depends on a latentvariable ϱ, which can be interpreted as the client’soverall recommendation intention. If ϱ > 0, we haveR = 1; if ϱ ≤ 0, we have R = 0. As theories and evi-dences on rater behavior suggest, reviews depend onthe net utility of the reviewers along with otheridiosyncratic factors.3 We hence model ϱ as follows.

. e;V; yð Þ ¼ U V; yð Þ þ e; ð3Þwhere ɛ stands for possible idiosyncratic factors thatcould affect the review. It is a random variable withcdf F(ɛ). Similarly, for neat analytical results, we letɛ follow a uniform distribution over the support[�1, w], so FðeÞ ¼ eþ 1

wþ 1. The support is chosen underthe same rationale as the case of ξ: when the client’sutility U(V, y) takes its minimum value �w (i.e.,when V = 0 and y = 1), ϱ(ɛ) ≤ 0 for any possible ɛ;when U(V, y) takes its maximum value 1 (i.e., whenV = 1 and y = 0), ϱ(ɛ) ≥ 0 for all ɛ’s. Again, neitherthe distribution nor the support of ɛ is critical. Ourmain results remain robust when extended to differ-ent distributions or expanded supports, as we showin detail in Appendix S2.As a result, the probability of the client writing a

positive review, given the outcome V and the client’seffort y, can be derived as

Pr R ¼ 1jV; yf g ¼ Pr . eð Þ[ 0jV; yf g¼ 1� F �U V; yð Þð Þ

¼ 1V¼1 � wy2 þ w

1þ w:

ð4Þ

In determining the payoff of the service provider,we model it endogenously in a general approach. Welet the market form a rational belief about the truetype of the service provider and reward the provideraccordingly. After observing the available signal(s)(e.g., the outcome V, the review R), the market formsa posterior belief a, which equals the posterior proba-bility of the service provider being a high type giventhe observed signal(s). We will articulate the forma-tion of a in detail in subsection 3.2. Given the belief a,the market rewards the provider with a payoff equalto amH þ ð1� aÞmL, where mL \mH so it is morerewarding to be viewed as a high-type provider.Notice that the payoff from the market is thus anabstract form of the present value of the provider’s

future payoff. It can be interpreted broadly, for exam-ple, as the monetary benefit rationally offered by athird-party authority, or as the willingness-to-pay offuture clients. Additionally, we let the service provi-der’s utility cost of exerting effort take the similar con-vex form as that of the client, that is, cx2, where c isthe provider’s effort cost coefficient (0\ c\mH).Once again, to simplify notation, we normalizemH ¼ 1 and mL ¼ 0 without loss of generality. As aresult, the service provider’s net payoff, given themarket belief a, can be written as

p x; að Þ ¼ amH þ 1� að ÞmL � cx2 ¼ a� cx2: ð5Þ

3.2. Equilibrium ConceptAs this study focuses on the type of collaborative ser-vices that the service provider not only determinesher own effort but also the effort level of her client,we consider that the provider decides both effortlevels x and y. (In subsection 6.1, we extend the modelto the general case that both the provider and the cli-ent jointly determine the client’s effort level y, andeach has a varying degree of influence. As we show,the main results continue to hold.) As a result, theactual strategic players in the model are the serviceprovider and the market. From the market’s stand-point, the effort levels x and y chosen by the serviceprovider are not observable.4 Instead, the market caninfer the true type of the provider only throughobservable information, such as the outcome V, thereview R, or both, which, in turn, depends on the hid-den actions taken by the provider. Such an informa-tion structure constitutes a typical signal-jamminggame (Fudenberg and Tirole 1986). Following thisframework, we let the market and the provider sharecommon knowledge about all model parameters,including the prior belief about the true providertype. In other words, the true type of the provider,which is essentially her underlying capability to deli-ver the service effectively, is not directly observable toeither the market or the provider herself, whereasthey share a common prior (probabilistic) belief aboutit. It is common in the classical literature on job per-formance and career concerns to assume that a playercannot observe her latent characteristic and share thesame prior belief with the market (e.g., Holmstrom1999). For simplicity, we use the uninformative priorsuch that the prior probability of the service provider

being a high type is 12, that is, Prfh ¼ Hg ¼ 1

2. Never-

theless, choosing a different prior other than 12 will not

qualitatively change our main results.The equilibrium concept we use is perfect Bayesian

equilibrium. In equilibrium, on one hand, the serviceprovider’s choice of effort levels are optimal given themarket’s belief; on the other hand, the market’s belief


is rational (according to Bayes’ rule) given the provi-der’s effort choice. In the subsequent analysis, we willstudy separate scenarios in which the market canobserve the outcome V only, the review R only, orboth the outcome and the review. We use S to repre-sent the signal that the market can observe. Depend-ing on different scenarios, S can be V, R, or {V,R}.Note that S is thus a random variable (or a pair of ran-dom variables) taking binary values.Upon observing the realized value of S, the market

rationally forms posterior belief about the true type ofthe service provider. Specifically, the market’s beliefa�S equals the posterior probability of the service pro-vider being a high type, conditional on the observedvalue of signal S and given the provider’s equilibriumeffort levels x� and y�. By Bayes’ rule,

a�S ¼ Pr h ¼ HjS; x�; y�f g¼ Pr Sjh ¼ H; x�; y�f g � Pr h ¼ Hf g=�

Pr Sjh ¼ H; x�; y�f g � Pr h ¼ Hf g

þ Pr Sjh ¼ L; x�; y�f g � Pr h ¼ Lf g�:

ð6Þ

Meanwhile, anticipating the market belief a�S, theservice provider makes an upfront decision ofthe optimal effort levels such that x� and y� maximizethe ex ante expectation of her net payoff (i.e., takingexpectation over the possible realization of the signalS conditional on the effort levels). Specifically,

x�; y�ð Þ ¼ arg max0� x;y� 1

Eh ES p x; a�S� �jh; x; y� ��

¼ arg max0� x;y� 1

Eh ES a�Sjh; x; y� �� cx2; ð7Þ

where the second equality holds by substituting in(5). Notice that although the effort level of the clienty does not directly enter the provider’s payoff func-tion (5), it does affect the provider’s expected payoffby influencing the realization of the signal S. There-fore, the service provider needs to optimize both xand y altogether, which introduces the strategicinteraction between these two decisions.Altogether, a perfect Bayesian equilibrium of this

signal-jamming game is hence a fixed pointfx�; y�; a�Sg that solves (6) and (7) simultaneously.

4. Analysis and Results

In this section, we first solve the equilibrium underseparate scenarios in which (i) the market observesthe outcome V alone as a signal, (ii) the marketobserves the review R alone as a signal, or (iii) themarket observes both the outcome and the review.We then derive formal results comparing the equilib-rium effort levels under these different scenarios,which further allow us to examine the equilibriumoutcomes in various dimensions such as the

effectiveness of service, the efficiency of the effortchoice, and the distinguishability of the true type ofthe service provider.

4.1. Outcome as a SignalWe first examine the benchmark scenario in whichthe market can observe the outcome V, whereas thereview R is unavailable, so S = V. To differentiatefrom the other two scenarios, we use the superscriptV to indicate the equilibrium solutions in this scenarioinstead of asterisk.In equilibrium, anticipating the equilibrium effort

levels chosen by the service provider, xV and yV, themarket rationally updates its posterior belief accord-ing to (6), which can be derived as

aV1 ¼ Prfh ¼ HjV ¼ 1; xV; yVg ¼ 11þl and aV0 ¼

Prfh ¼ HjV ¼ 0; xV; yVg ¼ 2�ðxV þ yVÞ4�ð1þlÞðxV þ yVÞ. Given

the market belief, the service provider optimizes theeffort levels to maximize her expected payoff, Ep,according to (7), where Ep ¼ aV0 þ 1þl

4 ðaV1 � aV0 Þ �ðx þ yÞ � cx2. Notice that the market forms its beliefwithout observing the actual effort, so the equilibrium

concept requires that aV1 and aV0 , and hence all xV’s

and yV’s included, be treated as constants when theprovider optimizes x and y. Denote

DaVðxV; yVÞ � aV1 � aV0 , we can write the first deriva-tive with respect to x and y as

@Ep@x

¼ 1þ l4

DaV xV; yV� �� 2cx; ð8Þ

@Ep@y

¼ 1þ l4

DaV xV; yV� �

: ð9Þ

Notice that @Ep@y is a constant, and it is easy to show

that this constant is always positive, that is,DaVðxV; yVÞ [ 0 for 8xV; yV (see Lemma A.1 inAppendix S1 for the proof). Therefore, the provider’sexpected payoff strictly increases in y. As a result, theoptimal choice of y is the upper bound of the client’seffort range, that is, yV ¼ 1. Consequently, the opti-mal choice of the service provider’s own effort level,xV, is the fixed-point solution to the first order condi-tion 1þl

4 DaVðxV; 1Þ � 2cxV ¼ 0 by (8), whenever suchan interior solution exists within [0, 1].Following the procedure outlined above, we can

formally derive the equilibrium effort levels when theoutcome is observed as a signal, as follows.

PROPOSITION 1. When the market observes the outcome Valone as a signal, for c [ 1

8, there is a unique equilibrium inwhich the service provider’s effort

xV ¼ 3� l2ð1þ lÞ �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið3� lÞ24ð1þlÞ2 � 1�l

4cð1þ lÞ

rand the client’s effort

yV ¼ 1.


PROOF. All proofs are detailed in Appendix S1. h

Proposition 1 shows that when only the outcomeis used as a signal, in equilibrium, the service pro-vider sets the highest possible effort level for theclient. Note that aV1 [ aV0 , which means a successfuloutcome gives the market more confidence tobelieve the service provider is a high type and isthus more rewarding to the provider. Hence, whenthe review is unavailable and the provider does notneed to take account of the client’s utility, shepushes the client’s effort to the maximum in orderto maximize the probability of getting a successfuloutcome. For the provider’s own effort, she tradesoff between the expected gain from market recogni-tion and the utility cost of exerting effort. As aresult, the optimal effort level of her own, xV, is aninterior solution between 0 and 1.It is worth emphasizing that we prove in Proposi-

tion 1 that there exists a unique equilibrium for theproposed signal-jamming game generically (i.e., aslong as c [ 1

8). In the extreme case when the serviceprovider’s effort cost coefficient is very small (i.e.,c\ 1

8), multiple equilibria could arise, among whichxV ¼ yV ¼ 1 is always an equilibrium. We findsimilar results for the other scenarios as well. Themultiple equilibria yield no closed-form full charac-terization and involve discussion on equilibriumrefinement, whereas the main results remain thesame, as we can show. Therefore, to deliver neatresults with clear implications and to avoid techni-cal distraction, in the main body of the study, wefocus on the generic cases when the service provi-der’s effort cost coefficient is not too small. InAppendix S3, we characterize the equilibria forsmall c’s in detail and show the main results extendrobustly.

COROLLARY 1. The equilibrium effort level of the serviceprovider, xV, is decreasing in her effort cost coefficient c,and increasing in the difference between the two types ofproviders 1 � l (i.e., decreasing in l).

Corollary 1 shows some interesting comparativestatics of the equilibrium effort. For example, as ldecreases and hence the capability gap between thetwo types of providers enlarges, the service provideris willing to work more diligently. This is because asthe gap between the two types of providers increases,the outcome becomes more revealing, so a successful(or failed) outcome signals more convincingly to themarket that the service provider is a high (or low)type. As a result, the marginal return for the serviceprovider to devote more effort to increase the proba-bility of a successful outcome also goes up, whichleads to a higher equilibrium effort level xV.

4.2. Review as a SignalWe next analyze the scenario in which the review R isavailable, whereas the outcome V, although stillobservable to the service provider and the client, isunobservable to the market. Thus, S = R. Again, todifferentiate from the other scenarios, we use thesuperscript R to indicate the equilibrium solutions inthis scenario instead of asterisk.The equilibrium can be derived following a similar

approach as described in subsection 4.1. A main dif-ference lies in formulating the likelihood function,PrfRjh; xR; yRg. Taking the expectation of the (condi-tional) probability of receiving a positive review(given the outcome V) in (4) over V, we have

Pr Rjh;xR;yR� ¼ Pr RjV¼ 1;yR�

Pr V¼ 1jh;xR;yR� þPr RjV¼ 0;yR

� Pr V¼ 0jh;xR;yR�

:

ð10ÞSubstituting (2) and (4) into (10), we can derive thelikelihood function, which leads to the equilibriummarket belief, aR1 ðxR; yRÞ and aR0 ðxR; yRÞ, according tothe Bayes’ rule in (6). Given the market belief, simi-lar as in subsection 4.1, the service provideroptimizes both x and y, and the equilibrium effortlevels are the fixed-point solution. DenotingDaRðxR; yRÞ ¼ aR1 � aR0 , we can summarize the equi-librium effort levels when the review is observed asa signal as follows.

PROPOSITION 2. When the market observes the review Ralone as a signal, for c [ 1

2Mð1Þ, there is a unique equi-librium in which the client’s effort yR ¼ minf1þl

8w ; 1gand the service provider’s effort xR is the unique solutionto M(x) = 2cx within the range of x 2 [0, 1], whereMðxÞ � 1þl

4ð1þwÞDaRðx; yRÞ.

Note that the function M(x) defined in Proposition2 originates from the first-order condition withrespect to x such that MðxRÞ ¼ 2cxR. As detailed inLemma A.2 in Appendix S1, the monotonicity of M(x)and @2

@x2 MðxÞ results in a single crossing of M(x) and2cx for x 2 [0, 1] when c is not too small, whichensures the existence and uniqueness of the equilib-rium effort xR.As Proposition 2 implies, when the review is

observed as the signal, the service provider no longeralways chooses the maximum effort level for the cli-ent. As long as the client’s cost coefficient w is not toosmall (i.e., w [ 1þ l

8 ), the optimal effort of the clientyR is set as an interior solution less than 1.

COROLLARY 2. The equilibrium effort of the service pro-vider, xR, is decreasing in her effort cost coefficient c andthe client’s effort cost coefficient w; the equilibrium effortof the client, yR, is (weakly) decreasing in w and


independent of c. While yR is (weakly) increasing in l,xR is decreasing in l when w � 1þl

8 and may changenon-monotonically in l when w [ 1þ l

8 .

Corollary 2 shows the comparative statics of theequilibrium effort. An interesting result is that as theclient’s effort becomes more costly, not only the cli-ent’s equilibrium effort yR decreases, the provider’sequilibrium effort xR also decreases. It thus impliessome degree of complementarity between the equilib-rium efforts of the provider and the client, as we willfurther explore. The possible non-monotonicity of xR

in l is also worth discussing. When w � 1þl8 (so

yR ¼ 1), xR is decreasing in l, similar to Corollary 1.

When w [ 1þ l8 (so yR ¼ 1þl

8w \ 1), on one hand, a

higher l reduces the difference between the two pro-vider types and thus the informational value of a pos-itive signal, which lowers the provider’s effortincentive; on the other hand, the provider can requirea higher effort level from the client as l increases,which, in turn, strengthens the provider’s own effortincentive. The two counteracting factors hence cause

the possible non-monotonicity, and xR may firstincrease and then decrease in l as l goes up.

4.3. Outcome and Review as SignalsWhen the market can observe both the outcome Vand the review R, both pieces of information will beincorporated into the rational expectation about thetrue type of the service provider. Under the baselinemodel, because the review does not convey additionalinformation regarding the true type of the providerbeyond what is already conveyed by the outcome, theequilibrium when both V and R are observable turnsout to be the same as when only V is available as thesignal (i.e., the equilibrium in subsection 4.1).Formally, such an equivalence originates from the

conditional independence of R on h given V, that is,Pr{R|V, h, x, y} = Pr{R|V, y}. In other words, giventhe realization of the outcome V, the probability ofreceiving a positive review no longer depends on thetrue type of the provider. As a result, Pr{V, R|h, x, y} = Pr{R|V, y}�Pr{V|h, x, y}, and in Bayesianupdating according to (6), the term Pr{R|V, y} cancelsout, and we have Pr{h = H|V, R, x, y} = Pr{h = H|V, x, y}. It means the posterior market belief whenboth V and R are observed will be the same as whenonly V is observed, independent of the value of R. Asa result, the equilibrium effort will be exactly thesame as the xV and yV derived in Proposition 1.In Section 5, we will extend the baseline model to

incorporate additional information regarding the truetype of the provider into the review. In that case,observing both signals will lead to different equilib-rium effort, which can deliver richer implications

regarding how client reviews could affect collabora-tive service provision.

4.4. Equilibrium ComparisonHaving obtained the equilibrium in the two scenarioswhere either the outcome or the review is observed asa signal, we next examine how the equilibrium effortdiffers across the two scenarios. We also compare theequilibrium performance of the service in terms ofeffectiveness, efficiency, and distinguishability.

PROPOSITION 3. The equilibrium effort levels of both theservice provider and the client are lower when the reviewis observed as a signal than when the outcome is observedas a signal. Specifically, for c [ 1

8, xR \ xV, andyR � yV with strict inequality when w [ 1þl

8 .

Proposition 3 shows that with the review observedas a signal, the service provider generally sets a lowereffort level for the client and devotes less effort her-self as well, in comparison to the case when the out-come is observed as a signal. To understand theresult that yR � yV, recall that the client gives thereview based on his net utility, which is increased bya successful outcome and decreased by his disutilityfrom exerting effort. Therefore, to maximize the prob-ability of receiving a positive review, the providerfaces the trade-off between a higher success probabil-ity and elevated effort disutility of the client. Theresult in Proposition 3 shows that the disutility con-cern generally dominates the success motivation, sothe provider typically requires lower effort from theclient compared to the case when only the outcomematters. Therefore, yR \ yV unless the client’s effort ismost costless (i.e., w is small).The comparison regarding the equilibrium effort of

the provider’s own is more subtle and intriguing toexplain. When optimizing her own effort, the serviceprovider faces the trade-off between convincing themarket of her capability and exerting costly effort. Indetermining the marginal benefit of improving marketrecognition from effort investment, two effects comeinto play: The first is the affirmative effect, that is, howgreatly an increased level of effort could improve thechance of attaining a positive signal. The second is theinformative effect, that is, how much information a posi-tive signal conveys to the market regarding the provi-der being a high type. When the review serves as asignal, there are two factors that reduce both the affir-mative and the informative effects. First, compared tothe outcome, the review is influenced by additionalfactors such as the client’s effort cost and many otherunobservables, all of which bring more uncertaintyand noise into the realization of the review value. Sec-ond, the equilibrium effort level of the client is lowerwhen the review serves as a signal, as just discussed.


Less effort from the client reduces the differencebetween the two types of providers in terms of theprobability of attaining a positive signal. Driven bythese two factors (i.e., additional uncertainty and lesseffort from the client), when the review serves as a sig-nal, the provider’s effort is less rewarding in generat-ing a positive signal, and moreover, a positive signalbecomes less informative about the true type of theprovider. As a result, both the affirmative and theinformative effects are reduced, so the marginal bene-fit of the provider’s effort investment decreases, lead-ing to a lower level of xR in equilibrium.It is worth noting that in the baseline model, both

the affirmative and the informative effects change inthe same direction across the two scenarios, causinga decisive comparison result. In addition, comparedto the outcome, the review leads to lower effortlevels of both the provider and the client. In thissense, the effort choices exhibit a strategic-comple-ment pattern in equilibrium. In Section 5, when weintroduce additional information about the providertype into the review, interestingly, the review maychange the affirmative and informative effects in theopposite directions, and the provider’s and theclient’s equilibrium effort levels may be strategicsubstitutes instead.Now that the review leads to less equilibrium effort

of both the provider and the client, we can immedi-ately compare the effectiveness of service, which wemeasure using the expected outcome in equilibrium,defined as

EV x�; y�ð Þ ¼ Eh E Vjh; x�; y�½ �f g: ð11Þ

PROPOSITION 4. The effectiveness of service is lower whenthe review is observed as a signal than when the outcome isobserved as a signal in that EVðxR; yRÞ\EVðxV; yVÞ.

We are also interested in investigating the efficiencyof the equilibrium effort the provider sets for the cli-ent in different scenarios.5 We define the efficient effortlevel of the client, ye, as the one that maximizes the cli-ent’s expected net utility, that is, the optimal effortlevel from the client’s own perspective. Specifically,

ye ¼ arg max0� y� 1

Eh;V U V; yð Þ½ �¼ arg max

0� y� 1EV x; yð Þ � wy2; ð12Þ

where EV is defined in (11) (Recall that the client’sutility gain from a successful outcome, u, is normal-ized to 1 for simplicity). It is easy to solve thatye ¼ minf1þ l

8w ; 1g, which is independent of the pro-vider’s effort x. Interestingly, the equilibrium effortlevel set for the client when the review is observedas a signal, yR, turns out to be efficient.

PROPOSITION 5. The client’s effort is at the efficient levelwhen the review is observed as a signal, whereas the cli-ent’s effort generally exceeds the efficient level when theoutcome is observed as a signal, that is, yR ¼ ye � yV

with strict inequality when w [ 1þ l8 .

Combining the results of Propositions 4 and 5, itbecomes clear that when the review serves as a signal,the equilibrium output is less success oriented;instead, it caters to the client to optimize his effortinput by sacrificing the effectiveness to a certaindegree. In contrast, when the outcome serves as a sig-nal, the client is pushed to work beyond his efficienteffort level.Another dimension we are interested in exploring

is the distinguishability of provider types. We want toexamine how accurately the market can tell the truetype of the provider in equilibrium under differentsignals. The natural means to measure the accuracy ofthe market’s posterior belief is the usual type I andtype II errors. In our context, we define the equilib-rium type I error, q�1, as the ex ante probability of mis-takenly believing a high-type provider as a low type,given the equilibrium effort levels. The equilibriumtype II error, q�2, is thus the ex ante probability of mis-takenly believing a low-type provider as a high type.By ex ante, we mean taking the expectation over possi-ble realized values of the signal S. We can formulatethe two types of errors as follows.

q�1 ¼ ES 1� a�Sjh ¼ H; x�; y�� ð13Þ

q�2 ¼ ES a�Sjh ¼ L; x�; y�� ð14Þ

It is noteworthy that because the prior belief is sym-metric and the posterior belief is formed rationallybased on the Bayes’ rule, it can be shown that theequilibrium type I and type II errors happen to be thesame in our context. This coincidence leads to a sim-ple and neat measure of the equilibrium distinguisha-bility of provider types, which we refer to as theequilibrium judgment error q�, where q� ¼ q�1 ¼ q�2.

6

Figure 1 illustrates the equilibrium judgment errorsunder different signals with different parameter val-ues. As we can see, qR [ qV in general, which meansthe review leads to a higher equilibrium judgmenterror than the outcome. This result can be explainedby the aforementioned two factors that reduce theinformative effect: the review brings in additionaluncertainty and also causes a lower equilibrium effortlevel of the client. It can be clearly seen from Figure 1how less effort from the client drives a higher equilib-rium judgment error: as the client’s effort cost coeffi-cient w goes up, the client’s effort yR decreases, andqR increases in consequence. Another noteworthy pat-tern in Figure 1 is the increase of judgment error in l.


As l increases and gets closer to 1, the low-type provi-der is closer to the high-type provider in terms of theinnate ability of successfully delivering the service.As a result, it becomes more difficult to tell apart thetwo types of providers, leading to a higher judgmenterror in equilibrium.

5. Review with Private Information

In the baseline model, the review R does not containany additional information about the provider typebeyond what has already been included in the out-come V. As discussed in subsection 4.3, this propertyleads to unchanged equilibrium results when thereview is observed along with the outcome. In thissection, we extend the baseline model by letting thereview contain additional information beyond theoutcome. The purpose of this extension is twofold.First, we want to show to what extent the main resultsfrom the baseline model are robust and if any newresults with richer implications will arise. Second, weare interested in shedding light on how the reviewcan further impact the collaborative service provisionwhen the outcome is already observable as a signal.Following the same setup of the baseline model,

now we assume that upon the completion of the ser-vice, the client can observe a private signal, ~h, thatsuggests the true type of the service provider. Thissignal is noisy in that it may correctly reflect the trueprovider type only with certain probability. LetPrf~h ¼ Hjh ¼ Hg ¼ rH, and Prf~h ¼ Hjh ¼ Lg ¼rL, rH; rL 2 ð0; 1�. In other words, the client may per-ceive a high-type (or low-type) provider as a hightype with probability rH (or rL). We consider thisnoisy signal (weakly) informative so that rH � rL,that is, a high-type provider is more likely to be per-ceived by the client as a high type than a low-typeprovider. It is then reasonable to assume that the

client will recommend the service provider only if heperceives her as a high type. Thus, we can modify theprobability of the client giving a positive review, pre-viously defined in (4), as

Pr R ¼ 1jh;V; yf g ¼ rh1V¼1 � wy2 þ w

1þ w: ð15Þ

Equation (15) implies that if the client receives apositive signal suggesting the provider is a hightype, he then gives a positive review with a proba-bility that is increasing in his net utility as modeledpreviously. In this sense, the baseline model is aspecial case with rH ¼ rL ¼ 1.Apparently, the change in the model does not affect

the equilibrium results when only the outcome isobserved by the market. Therefore, the results in sub-section 4.1 continue to hold under this extendedmodel. On the other hand, it may affect the equilib-rium results when the review alone is available as thesignal and when both the review and the outcome areobservable to the market. In what follows, we presentthe results in these two scenarios under this extendedmodel. Throughout this section, we add a tilde ( )to indicate the equilibrium solutions under thisextended model.

5.1. Review as a SignalThe equilibrium efforts can be derived following thesame approach outlined in subsection 4.2. DenotingD~aRð~xR; ~yRÞ ¼ ~aR1 � ~aR0 , we are able to solve the equi-librium under this extended model as follows.

PROPOSITION 6. When the market observes the review Ralone as a signal, for any 0\ rL � rH � 1, ifc [ 1

2~Mð1Þ, there is a unique equilibrium in which the

client’s effort ~yR ¼ minf rH þ rLl4wðrH þrLÞ ; 1g and the service

provider’s effort ~xR is the unique solution to ~MðxÞ ¼ 2cx

within the range of x 2 [0, 1], where ~MðxÞ� rH þ rLl

4ð1þwÞ D~aRðx; ~yRÞ.

Proposition 6 shows that the same structure of theequilibrium solution from the baseline model contin-ues to hold in this extended model. In particular, forany 0\ rL � rH � 1, we can prove the similar prop-erties on the shape of the ~MðxÞ function, which ensurea single crossing of ~MðxÞ and 2cx, and hence establishthe existence and uniqueness of ~xR.Proposition 6 lays the foundations for the robust-

ness of the main results in subsection 4.4 whenextended here. Next, we compare the equilibriumeffort ~xR and ~yR and the service effectiveness, mea-sured by EVð~xR; ~yRÞ, with their counterparts when Vis observed as a signal. We summarize all the resultsin Table 1, and discuss the key findings in more detailafterward.

0 0.2 0.4 0.6 0.8 10.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

μ

Judg

emen

t err

or

w

ρV

ρR, w=0.15

ρR, w=0.2

ρR, w=0.25

Figure 1 Illustration of Equilibrium Judgment Error (c = 0.15)


PROPOSITION 7. Comparing the equilibrium effort andthe service effectiveness ~xR, ~yR, and EVð~xR; ~yRÞ with xV,yV, and EVðxV; yVÞ, we have the following results assummarized in Table 1.

As Table 1 (the first row) shows, we first comparethe equilibrium effort of the client (~yR and yV) undergeneral values of rH and rL. The result that thereview as a performance signal leads to a lower, yetmore efficient, effort level for the client remainsrobust. In particular, when rH ¼ rL, ~yR reaches theefficient level of effort ye, which is consistent with theresult under the baseline model (i.e., Proposition 5).Interestingly, when the client’s private signalbecomes informative (i.e., rH [ rL), we have~yR [ ye. With an informative private signal, the cli-ent’s review is more likely to reflect the true type ofthe provider and less sensitive to the client’s utility. Ithence reduces the incentive of the provider to cater tothe client by prescribing a lower effort level inexchange for higher satisfaction. As a result, the pro-vider requires the client to put in more effort than themost efficient level for him. Nevertheless, as long asthe provider is still concerned about the client’s util-ity when the review serves as a performance signal,~yR remains more efficient than yV in general.We next compare the equilibrium efforts of the pro-

vider (~xR and xV) in two special cases, which allow usto derive formal results with representative and gener-alizable implications. The first case is when the client’sprivate signal is not informative so that rH ¼ rL � r,which subsumes the baseline model as r = 1. The sec-ond case is when the client’s private signal is informa-tive and symmetric so that rH ¼ c and rL ¼ 1 � c,c 2 ½12 ; 1�. Recall that rh ¼ Prf~h ¼ Hjhg. In this sense,the symmetric structure indicates that with probabilityc, the client’s private signal correctly reflects the truetype of the service provider. Note that c � 1

2 so that

rH � rL, meaning that the client’s private signal isinformative or “correct” to a large extent.As Table 1 (the second row) shows, the result that

the review as a performance signal leads to less equi-librium effort of the provider continues to hold ingeneral: ~xR \ xV holds for all r’s in the first case, andin most regions in the second case. An interestingaspect worth highlighting is that ~xR increases with theprecision of the client’s private signal c, and once c islarge enough, it is possible that ~xR exceeds xV. Thisnew result can be well understood based on the inter-action of the two effects that govern the provider’sincentive of effort investment. As the client’s privatesignal becomes more precise (i.e., as c increases), theaffirmative effect is partially weakened because a lowtype will be less likely to get a positive review any-how, even if the outcome is successful. On the con-trary, with precise private observation embedded inthe review, a positive review becomes highly informa-tive about the provider type. Hence, the informativeeffect significantly increases. As c becomes largeenough, the increase of the informative effect domi-nates the reduction of the affirmative effect, leading tohigher marginal benefit for the provider’s effortinvestment and hence higher equilibrium effort.Recall that in the baseline model, the review brings

down both the affirmative and the informative effectsalong the same direction. In contrast, when the reviewcontains additional information about the providertype, it may change the two effects in the oppositedirections, which drives the relative magnitude of theequilibrium effort one way or another. It is also worthemphasizing that because ~yR � yV holds for anyrL � rH, when the review is highly informative, itcould be the case that ~xR compares to xV in the oppo-site direction as ~yR compares to yV. In other words,with the review rather than the outcome as theperformance signal, the provider strategically lowers

Table 1 Equilibrium Comparison When Review Contains Private Information (c > 18)

Uninformative private signalrH ¼ rL ¼ r ðr 2 ð0; 1�)

Informative symmetric private signalrH ¼ c, rL ¼ 1 � c ðc 2 ½12 ; 1�)

y� yV � ~yR � ye for any 0\ rL � rH � 1(The last inequality holds strictly if and only if rH [ rL)

x�(i) ~xR is increasing in r; (i) ~xR is increasing in c;

(ii) ~xR \ xV , ∀r2(0, 1] (ii) ~xR [ xV if l [ ~l and c [ ~c;y~xR � xV otherwise

EV ðx �; y �Þ EV ð~xR ; ~yR Þ\ EV ðxV ; yV Þ, ∀r2(0, 1] EV ð~xR ; ~yR Þ [ EV ðxV ; yV Þ if w \ w , l [ l, and c [ c;z

EV ð~xR ; ~yR Þ � EV ðxV ; yV Þ otherwise

Notes: yThere exist such thresholds ~lðw ; cÞ 2 ð0; 1Þ and ~cðl; w ; cÞ 2 ð12 ; 1Þ.zThere exist such thresholds wðcÞ 2 ð0; 1Þ, lðw ; cÞ 2 ð0; 1Þ and cðl; w ; cÞ 2 ð12 ; 1Þ.


the effort level required for the client, but she worksmore diligently herself in compensation. In this sense,the collaborative effort decisions could exhibit astrategic-substitute pattern when the client review ishighly informative, which enriches the strategic-complement pattern found under the baseline model.We further compare the service effectiveness,

EVð~xR; ~yRÞ and EVðxV; yVÞ. As Table 1 (the third row)shows, we find the similar result that the review gen-erally leads to less effectiveness of service compared tothe outcome, that is, EVð~xR; ~yRÞ\EVðxV; yVÞ in gen-eral. Nevertheless, such a relationship can be reversedwhen the review contains highly precise private obser-vation of the client (i.e., in the second case with c suffi-ciently large), just like the comparison between ~xR andxV as discussed above. As Figure 2a (the dark greyregion) plots, when w is small (i.e., the client’s effort isnot too costly) and l is large (i.e., the ability gapbetween the two types of providers is small enough),EVð~xR; ~yRÞ could exceed EVðxV; yVÞ for large c’s.To demonstrate that the results derived from the

two special cases shown in Table 1 are representativeand general, we further solve the equilibrium numeri-cally for all different values of rH and rL(0\ rL � rH � 1). Figure 2b depicts the comparisonresult of ~xR versus xV over the plane of rH and rL.Notice that the two special cases correspond to the twodiagonals. When moving from the center towards thelower right corner of the figure, rH increases and rLdecreases, representing that the client’s private signalbecomes more and more informative or accurate. Ascan be clearly seen from Figure 2b, ~xR exceeds xV onlyaround the lower right corner, which is consistent withthe implications from the two special cases in Table 1.

5.2. Outcome and Review as SignalsUnder this extended model, when both the outcomeV and the review R are observable to the market as

performance signals, the equilibrium solution will bedifferent from when only V is available. The reason isthat the conditional independence of R on h given Vas in (4) no longer holds under this extended model.According to (15), the probability of receiving a posi-tive or negative review, even given the outcome V,still depends on the provider type h. Thus, Pr{V,R|h, x, y} = Pr{R|V, h, y}�Pr{V|h, x, y}. Substitute thislikelihood function into (6), and we can easily see thatthe posterior belief does depend on the realized val-ues of both V and R.We can follow the same approach described previ-

ously to derive the equilibrium solution here. Theonly challenge lies in that the first-order conditions nolonger separate the optimal solution of y from theoptimal solution of x as in the previous scenarios.Instead, we need to solve two simultaneous equationsof higher order involving both x and y, which yieldsno closed-form analytical solution. Nevertheless, wecan solve the equilibrium numerically under differentparameter values. Figure 3 illustrates the equilibriumefforts, ~xVR and ~yVR, in the case of symmetric informa-tive signal such that rH ¼ c and rL ¼ 1 � c(c 2 ½12 ; 1�), in comparison to the equilibrium effortsunder the other two scenarios. Consistently, we usethe superscript VR to denote the equilibrium solutionwhen both V and R are available as signals.As Figures 3a and b show, when c is relatively

small, ~yVR takes the corner solution so that~yVR ¼ 1 ¼ yV and ~xVR ¼ xV. The most surprisingresult revealed in Figures 3a and b is that both ~xVR

and ~yVRdecrease as c becomes larger, changing in theopposite direction as ~xR and ~yR. In other words, whenboth the outcome and the review are observable bythe market, as the review itself is more informativeabout the true provider type, there is less incentive forthe service provider to devote effort herself and torequire the client to work diligently—in fact,

Equilibrium Comparison with γ = 1(a) (b)

μ

(w =

Figure 2 Equilibrium Comparison When Review Contains Private Information (c = 0.15)


achieving a successful outcome is less desirable forthe service provider in this case. This counterintuitiveresult originates from the non-monotonicity of theinformative effect under a bivariate signal structure.When the market signal is univariate (i.e., either V orR alone is observed), a positive signal is always posi-tively informative in that it suggests the service provi-der is more likely to be a high type than a low type;however, with a bivariate signal structure (i.e., both Vand R are observed), this may not always be the case.For example, if the service provider turns out to be alow type, with a highly accurate private signal of theclient (i.e, c close to 1), the provider will most likelyreceive a negative review; in this case, the providermight be even better off with a failed outcome than asuccessful outcome. This is because the combinationof {V = 1, R = 0} could convey a stronger messagethat the provider is a low type than the combinationof {V = 0, R = 0}, considering that receiving a nega-tive review despite a successful outcome suggests tothe market that the client might have observed a nega-tive private signal, which is supposedly accurate.Because of such non-monotonicity, the overallexpected benefit of achieving a successful outcomethrough costly effort investment significantly reduceswhen c increases under the bivariate signal structure,resulting in the interesting decreasing pattern of both~xVR and ~yVR found in Figures 3a and b.Given that the equilibrium effort levels ~xVR and ~yVR

both decrease as the review becomes more informa-tive, it can be expected that the effectiveness of ser-vice, measured as EVð~xVR; ~yVRÞ, also decreases in cwhen c is large, as we show in Figure 3c. In fact, whenthe review contains accurate information about theprovider type, the scenario with both the outcomeand the review as signals leads to the lowest outcomeexpectation among all three scenarios.We further plot the equilibrium judgment error ~qVR,

together with ~qR and qV in Figure 4, where 4a showshow they change in l, and 4b in c. Surprisingly, con-trary to the intuition that more information typicallyleads to better distinguishability, as Figure 4 shows,

with two pieces of information observable (i.e., both Vand R), ~qVR could end up higher than ~qR, the equilib-rium judgment error when only one piece of informa-tion is observable. The reason is the lower effort levelsstrategically chosen by the service provider in equilib-rium, as discussed previously. This interesting resultthus serves as a good illustration of how strategicinterplay could garble the information effectively con-veyed under a complex information structure.As we can also see in Figure 4, qV is low when l is

small, indicating that the outcome leads to a highdegree of distinguishability only when the inherentability gap between the two types of providers islarge. Recall the results in Figure 1 that the reviewgenerally leads to a greater error. In contrast, asshown in Figure 4, with additional information aboutthe provider type, the review alone can result in thelowest equilibrium judgment error among all threescenarios, especially when l and c are large. Alongthis line, summarizing the analysis in this sectionsheds light on the effects of client reviews on serviceperformance: with reasonably accurate extra informa-tion about the provider type, client reviews could leadto superior performance of collaborative services withbetter distinguishability of provider types, greater ser-vice effectiveness, and relatively more efficient effortrequirement for the client.

6. Extensions

6.1. Client’s Effort Jointly DeterminedIn this section, we extend the model to relax theassumption that the service provider solely determi-nes the effort level of the client in the collaborativeservice. We now consider the general case that boththe provider and the client jointly determine theeffort level of client, and we allow the two partiesto have their respective degrees of influence, whichcan vary as a model parameter. Such a generaliza-tion thus subsumes the two special cases wheneither the provider or the client alone fully determi-nes the client’s effort.

(a) (b) (c)

Figure 3 Equilibrium Comparison with rH ¼ c and rL ¼ 1 � c (c = 0.15, w = 0.25, l = 0.7)


Specifically, we let the overall effort level the clienteventually exerts, y, be jointly determined by a levelrequired by the service provider, y1, and a level cho-sen by the client himself, y2, as follows.

y ¼ �y1 þ 1� �ð Þy2; �; y1; y2 2 0; 1½ �: ð16ÞHere, k 2 [0, 1] captures the relative strength of influ-ence of the two parties. If k = 1, y ¼ y1, so the serviceprovider fully determines y, and it hence reduces tothe original model. When k = 0, y ¼ y2, so it is totallyup to the client to decide his own effort, which isanother special case of our interest. The service provi-der first decides y1, and the client chooses y2 afterobserving the required level y1. As previously, bothy1 and y2 are decided and invested upfront before theoutcome realizes. To differentiate from the previoussections, we add a hat (^) to indicate the equilibriumsolutions in this extended model.In determining his optimal effort choice y�2, the cli-

ent maximizes the ex ante expectation of his net utilityUðV; yÞ ¼ 1V¼1 � wy2, and therefore,

y�2 y1ð Þ ¼ arg max0� y2 � 1

Eh E Vjh; x�; �y1 þ 1� �ð Þy2½ �f g� w �y1 þ 1� �ð Þy2ð Þ2: ð17Þ

The service provider sets the optimal y�1 by maxi-mizing her expected payoff according to (7), wherey ¼ �y1 þ ð1� �Þy�2ðy1Þ. Notice that the optimaloverall effort level y for the client (if he could fullydecide) would be the efficient effort level ye asdefined by (12); the optimal y for the service provi-der (if she could fully decide) would simply bewhat is derived from the original model, y�. Hence,

the resulting overall effort level of the client in thisextended model, y�, is a balance between y� and ye,depending on the two parties’ relative strength ofinfluence, k. When the provider has strong influ-ence, for example, if � [ y� [ ye, the provider willset y�1 ¼ y�=�, anticipating that the client will try tolower the overall effort as close to ye as possible bysetting y�2 ¼ 0; consequently, y� ¼ y�. When the cli-ent has strong influence, for example, if�\ ye \ y�, the provider could actually set y�1 asany value between maxfye þ�� 1

� ; 0g and 1, becausethe client will choose y�2 ¼ 1

1�� ðye � �y�1Þ to alwaysbring the overall effort level y� equal to ye eventu-ally. In other cases, for example, if ye \ �\ y�, y�

will simply be equal to k as a result of y�1 ¼ 1 andy�2 ¼ 0.We first extend the baseline model to incorporate

the jointly determined effort structure. The equilib-rium effort when either the outcome or the review isobservable as a signal is summarized in Table 2 (thefirst two columns). When the review is observed as asignal, recall that Proposition 5 shows the optimal ychosen by the service provider, yR , turns out to beexactly the same as the efficient effort level the clienthimself would choose, ye. In this case, the provider’sand the client’s strategies completely align. Therefore,in this extended model, regardless of the value of k,the overall level of the client’s effort remains the sameas the one derived from the baseline model, that is,yR ¼ yR ¼ ye ¼ minf1þ l

8w ; 1g. When the outcome isobserved as a signal, however, the provider’s and theclient’s optimal choices of y differ, and yV depends onthe value of k. If k = 1, yV reduces to a constant 1,which equals yV in the baseline model. If k = 0, the

(a) (b)

Figure 4 Comparison of Equilibrium Judgment Errors (c = 0.15, w = 0.25)


client himself fully determines his effort and hencechooses the efficient effort level. As a result, yV

reduces to yeð¼ yR ¼ yRÞ. On the other hand, theequilibrium effort levels of the provider in thisextended model (i.e., xV and xR characterized inTable 2) extend naturally from the baseline model.While the value of x� could change as y� differs fromthe baseline model in some cases, the functional rela-tionship between x� and y� remains the same. Com-paring xV and xR (yV and yR) in this extended model,we can show that the same result derived from thebaseline model continue to hold, as summarized bythe following proposition.

PROPOSITION 8. In the extended model with the client’seffort jointly determined by both parties, for c [ 1

8,xR \ xV for any k 2 [0, 1], and yR � yV with strictinequality when � [ 1þ l

8w .

We further apply the jointly determined effortstructure to the case when the client incorporatessymmetric private signal into the reivew, as discussedin Section 5. As shown in the rightmost column of

Table 2, when k = 1, ~yR reduces to

~yR ¼ minfcþð1� cÞl4w ; 1g as expected; when k = 0, ~yR

reduces to ye ¼ minf1þl8w ; 1g. Moreover, ~xR extends

naturally from Section 5. The results regarding thecomparison between ~xR and xV ð~yR and yV) continueto hold under this extended model, as follows.

PROPOSITION 9. In the extended model with the client’seffort jointly determined by both parties, when the clientincorporates symmetric private information into thereview (i.e., rH ¼ c and rL ¼ 1 � c), (i) ~yR � yV withstrict inequality when � [ cþð1� cÞl

4w ; (ii) for c [ 18,

there exists (c, w, l, k) such that for a certain threshold~cðc; w; l; �Þ 2 ð12 ; 1Þ, ~xR � xV when c � ~c, and ~xR [xV when c [ ~c.

In sum, the analysis in this section shows that whenextended to allow the client to determine his effortinput jointly with the service provider, our mainresults continue to hold. In the extreme case when theclient solely determines his own effort (i.e., k = 0), allthe main results with respect to the provider’s effort,x�, remain robust; meanwhile, the equilibrium effortof the client, y�, reduces to a simple case in which italways equals the efficient effort level, no matter whatsignal is observed by the market. In this sense, study-ing the general case that the provider (at least to someextent) decides the client’s effort level in collaborativeservices allows us to further examine how differentsignals could affect the client’s effort and to explorethe additional strategic correlation between the twoeffort decisions.

6.2. Client’s Effort ObservableThus far, we consider the client’s effort as unobserv-able to the market. There is another possible

Table 2 Equilibrium Effort under Jointly Determined y

V as a signalR as a signal

(w/o private information)R as a signal

(w/ private information, rH ¼ c, rL ¼ 1 � c)

yV ¼

1 if 1þl8w � 1

1þl8w if �\ 1þl

8w \1

� if 1þl8w ��

8>>><>>>:

yR ¼1 if 1þl

8w � 1

1þl8w if 1þl

8w \1

8<:

~yR ¼

1 if w� 1þl8

1þl8w if 1þl

8 \w� 1þl8�

� if 1þl8� \w� cþð1�cÞl

4�

cþð1�cÞl4w if w[ cþð1�cÞl

4�

8>>>>>>>><>>>>>>>>:

x � is the unique solution within [0, 1] to the following equations (c > 1/8)

K ðx V ; y V Þ ¼ 2cxV Mðx R ; y R Þ ¼ 2cxR ~Mð~xR ; ~yR Þ ¼ 2c ~xR

where

Kðx; yÞ ¼ 1� l2½4� ð1þ lÞðxþ yÞ� :

Mðx; yÞ ¼ ðxþ yÞ þ 2wð1� y2Þð1þ lÞðxþ yÞ þ 4wð1� y2Þ �

2ð1þ wÞ � ðxþ yÞ � 2wð1� y2Þ4ð1þ wÞ � ð1þ lÞðxþ yÞ � 4wð1� y2Þ

1þ l4ð1þ wÞ :

��

~Mðx; yÞ ¼ cðxþ yÞ þ 2cwð1� y2Þðcþ ð1� cÞlÞðxþ yÞ þ 2wð1� y2Þ �

2ð1þ wÞ � cðxþ yÞ � 2cwð1� y2Þ4ð1þ wÞ � ðcþ ð1� cÞlÞðxþ yÞ � 2wð1� y2Þ

cþ ð1� cÞl4ð1þ wÞ :

��


scenario that the client may convey informationabout his effort in his review, and as a result, the cli-ent’s effort could be observable to the market whenthe review is available as a signal. In order to showthat our model can accommodate such possibilityand the main results remain robust, we conduct anextension along this direction. Due to page limita-tion, we include the detailed analysis and results inAppendix S4. We briefly discuss the intuition below.To differentiate from the original results, we add adot on top of the equilibrium solutions under thisextended model.We follow the baseline model with the only dif-

ference that the client’s effort y is now observed bythe market when the review R serves as a signal.This difference leads to a major change in the equi-librium concept: Now that y is directly observed,the market incorporates this information in formingits rational belief about the provider type and “fig-uring out” the provider’s equilibrium effort _x�.Specifically, given any choice of y, a perfect Baye-sian equilibrium is a pair f _x�ðyÞ; _a�ðyÞg such that_x�ðyÞ is optimal for the provider given the marketbelief _a�ðyÞ, while _a�ðyÞ is rational according toBayes’ rule given the provider’s chosen effort _x�ðyÞ.Anticipating such equilibrium outcomes, the serviceprovider chooses _y� that maximizes his expectedpayoff ex ante, which leads to his own equilibriumeffort _x�ð _y�Þ.As we find, the equation defining _xR given y

remains the same as previously, and therefore, _xR and_yR follow the same functional relationship. The provi-der’s optimization of y results in _yR that minimizesher own effort input _xRðyÞ among all possible y’s. As aresult, _xRð _yRÞ � _xRðyRÞ ¼ xR, that is, the equilibriumeffort of the provider in this extended model _xR is nogreater than that in the original model xR. Notice thatthe equilibrium when the outcome V serves as a sig-nal is unaffected in this extension. Comparing _xR andxV ( _yR and yV), we can show that _yR � yVð� 1Þ and_xRð� xRÞ\ xV continue to hold.We further extend the case when the client incorpo-

rates private information into the review to allow thepossibility of y being observable. As we find, similarresults continue to hold: when the client’s privateinformation is precise enough (i.e., when c is suffi-ciently large), it is possible that _~xR [ xV, whereas_~yR � yV always holds, resulting in a strategic-substi-tute pattern between the two effort decisions.

7. Conclusion

In this study, we take the first step to study the provi-sion of collaborative services under online reviews.Utilizing a signal-jamming model, we endogenouslyanalyze how effectively the client review conveys

information about the underlying capability of theservice provider and examine the interplay betweensuch endogenous informativeness and the strategicactions of the provider. Our modeling results providerich managerial implications for information systemsdesigners, top management and authorities, serviceproviders, and clients as well.A key implication to information systems designers

is that the information being collected and madeavailable changes the strategic behavior of systemusers and hence impacts the performance the systemsaim to achieve, especially in the context of servicemanagement. In fact, the common wisdom that moreinformation is better may not always hold. As weshow, when both the client review and the serviceoutcome are observable to the public, the motivationfor service providers to devote effort could be unex-pectedly hurt. As a result, two pieces of informationmay lead to lower effort levels and hence inferior per-formance (i.e., effectiveness of service, distinguisha-bility of provider types) than one piece ofinformation alone. Therefore, our findings under-score the crucial importance of endogenously exam-ining the strategic consequences of the proposedinformation structure in designing information sys-tems for service management.For top management and authorities (e.g., man-

agers of private tutoring companies, administratorsof a school district) to deploy evaluation systems toincentivize subordinate service providers toimprove their service provision, our study empha-sizes that such decisions need to be context specificand could differ greatly depending on the servicecharacteristics. In general, two dimensions of theservice characteristics are particularly important toconsider: the ability difference among service provi-ders, and how accurately clients can tell the differ-ence among providers after the service. Our resultsshow that reviews serve as a satisfactory perfor-mance indicator when the difference among serviceproviders are not too large (e.g., for industries whenall service providers need to pass relatively strictqualification or certification processes); otherwise,service outcomes would be a better choice in gen-eral. For services in which clients are able to rela-tively accurately tell the difference among providers(e.g., mature adults, experienced learners), clientreviews could lead to superior effects in multipledimensions; in contrast, the effects of reviews maybe significantly impaired if, for example, the clientsare mainly young children.Our modeling results provide further guidelines

for collaborative service providers in determiningtheir effort strategies. We suggest that effort input isthe most rewarding when reviews are available andclients incorporate accurate private observations into


their reviews. In this case, it is wise for service provi-ders to refrain from pushing clients to overwork andmeanwhile to compensate with excessive effort them-selves. Finally, our study also provides implicationsfor clients who review their service providers. As weshow, reviews with more informative private signalsgenerally lead to more desirable results in variousdimensions. In this sense, as clients write reviews,whenever possible, they should also rely on their per-sonal observations about the provider’s capabilitythan merely their utility based on the service outcomeand their effort.As an initial attempt, this study is not without limi-

tations, which point to interesting directions forfuture research. First, we focus only on the services inwhich the service outcome is beyond the manipula-tion of the service provider. Once the provider canstrategically manipulate the service outcome per-ceived by the client, this additional strategic decisionwill naturally lead to interesting new findings. Sec-ond, we do not model the pricing decision of the ser-vice provider. As the motivating example of ourstudy, the industry of educational and tutoring ser-vices consists of mostly small service providers, andthere is usually a prevailing price rate for providing acertain type of service in each particular geographicarea (Franchisehelp 2016). Therefore, service provi-ders typically act as price takers. Besides, in manyoccasions, the clients who write reviews do not incurthe service cost directly,7 so the price of the servicedoes not enter the client’s utility function to affect thereview. Based on these considerations, we choose toleave the pricing of the service as exogenous in orderto focus on the strategic interplay between the effortlevels chosen for both the provider and the client.Nevertheless, allowing the provider to price endoge-nously will be an important and interesting futureresearch direction. Third, we show that a bivariatesignal structure may lead to counterintuitive equilib-rium outcomes through numerical analysis. A generalmodeling study on the strategic interplay under mul-tivariate signal structure in a signal-jamming gamewould thus be a challenging yet intriguing directionwith theoretical significance to information eco-nomics.

Acknowledgments

The authors contribute equally and are listed in alphabeticalorder. Lizhen Xu is the corresponding author. The authorsthank Dr. Vijay Mookerjee, the senior editor, and twoanonymous reviewers for their insightful and constructivecomments, which have greatly improved this study. Theauthors also thank the session participants at INFORMSAnnual Meeting (2013) and POMS Annual Conference(2016) for their helpful feedback.

Notes

1In this study, we focus on the case in which the outcomeof the service is objective and beyond the manipulation ofservice providers (e.g., passing a standardized test, achiev-ing preset goals). Other cases in which service providersmay be able to manipulate the service outcome (e.g., bylowering the difficulty of the test) involve additionalstrategic interplay beyond the scope of this study and aretherefore left for future research.2The client can be viewed as the representative of a group.Our model can also be extended to the case of a finitenumber of clients, and the main results will continue tohold qualitatively.3For example, Wherry and Bartlett (1982) develop a psy-chological theory decomposing rating into a systematiccomponent and a random component. Kane (1994) identi-fies multiple idiosyncratic factors (e.g., halo effect, assimi-lation or contrast effects, primacy or recency effects) thatcould bias ratings. Li and Hitt (2010) find empirical evi-dence that customer ratings are correlated more closelywith the net utility that customers derive from the productthan with product quality itself. Net utility-based rating iscommonly adopted in theoretical work (e.g., Jiang andGuo 2015, Kuksov and Xie 2010).4Our results can be further extended to the case when y isobservable to the market along with online reviews, as wediscuss in subsection 6.2.5It would also be interesting to examine the efficiency ofthe provider’s own effort choice. Nevertheless, the defini-tion of the efficient effort level of the service provider isindecisive in our context. It depends on how to interpretthe market rewards so as to define the overall social wel-fare. The result will also depend on the values of mH andmL (which are normalized for simplicity) relative to othermodel parameters. For these reasons, we choose to leaveout this part of analysis to avoid sidetracked discussions.6If the prior belief is not symmetric, the equilibrium type Iand type II errors themselves may differ. However, thegeneral trend regarding the comparison result across thetwo scenarios will remain the same.7For example, in professional training or consulting projects,while companies pay for the services, their employees dealwith the details and evaluate the service providers. Simi-lar examples exist in the education industry: for instance,U.S. federal government established the Supplemental Edu-cational Services (SES) to provide free after-school tutoringto low-income students who struggle academically.Through SES, parents choose any private providers on thestate’s vendor lists and the school districts pay the costs oftutoring.

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Supporting InformationAdditional Supporting Information may be found in theonline version of this article:

Appendix S1: Proofs.Appendix S2: Different Distributions for ξ and ɛ.Appendix S3: Results When c is Small.Appendix S4: Results for Sections 6.2.


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